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A recollement construction of Gorenstein derived categories |
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| Authors: | Peng Yu |
| Affiliation: | Department of Elementary Education, Changsha Normal University, Changsha 410100, China |
| Abstract: | We first give an equivalence between the derived category of a locally finitely presented category and the derived category of contravariant functors from its finitely presented subcategory to the category of abelian groups, in the spirit of Krause’s work [Math. Ann., 2012, 353: 765–781]. Then we provide a criterion for the existence of recollement of derived categories of functor categories, which shows that the recollement structure may be induced by a proper morphism defined in finitely presented subcategories. This criterion is then used to construct a recollement of derived category of Gorenstein injective modules over CM-finite 2-Gorenstein artin algebras. |
| Keywords: | Recollements functor categories derived categories Gorenstein algebras weak excellent extension locally finitely presented categories |
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